Recent questions tagged gate2019-ec

The value of the integral $ \displaystyle{}\int_{0}^{\pi} \int_{y}^{\pi}\dfrac{\sin x}{x}dx\: dy ,$ is equal to __________.

Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundament...

Radiation resistance of a small dipole current element of length $l$ at a frequency of $3$ GHz is $3$ ohms. If the length is changed by $1\%$, then the percentage change ...

In the circuit shown, $V_{s}$ is square wave of period $T$ with maximum and minimum values of $8\: V$ and $-10\: V$, respectively. Assume that the diode is ideal and $R_{...

Consider the line integral$$\int_{c} (xdy-ydx)$$the integral being taken in a counterclockwise direction over the closed curve $C$ that forms the boundary of the region $...

Consider a six-point decimation-in-time Fast Fourier Transform $(FFT)$ algorithm, for which the signal-flow graph corresponding to $X $ is shown in the figure. Let $W_{6}...

It is desired to find a three-tap casual filter which gives zero signal as an output to an input of the form$$x[n]= c_{1}exp\left(-\dfrac{j\pi n}{2}\right)+c_{2}\left(\df...

In the circuit shown, if $v(t)=2 \sin(1000\: t)$ volts, $R=1\:k \Omega$ and $C=1\:\mu F,$ then the steady-state current $i(t)$, milliamperes (mA), is$\sin(1000\: t)+ \cos...

Consider a causal second-order system with the transfer function$$G(s)=\dfrac{1}{1+2s+s^{2}}$$with a unit-step $R(s)=\dfrac{1}{s}$ as an input. Let $C(s)$ be the correspo...

The block diagram of a system is illustrated in the figure shown, where $X(s)$ is the input and $Y(s)$ is the output. The transfer function $H(s)=\dfrac{Y(s)}{X(s)}$ is$H...

Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the syst...

A single bit, equally likely to be $0$ and $1$, is to be sent across an additive white Gaussian noise (AWGN) channel with power spectral density $N_{0}/2.$ Binary signali...

The quantum efficiency $(\eta)$ and responsivity $(R)$ at wavelength $\lambda \:(\text{in}\: \mu m)$ in a p-i-n photodetector are related by$R= \frac{\eta \times \lambda}...

Two identical copper wires $W1$ and $W2$ placed in parallel as shown in the figure, carry currents $I$ and $2I$, respectively, in opposite directions. If the two wires ar...

The dispersion equation of a waveguide, which relates the wavenumber $k$ to the frequency $\omega$ is$$k(\omega)= (1/c) \sqrt{\omega^{2}-\omega_{\circ}^{2}}$$where the sp...

In the circuit shown, the breakdown voltage and the maximum current of the Zener diode are $20\:V$ and $60\:mA$, respectively. The values of $R_{1}$ and $R_{L}$ are $200\...

The state transition diagram for the circuit shown is

In the circuits shown the threshold voltage of each $\text{nMOS}$ transistor is $0.6\:V.$ Ignoring the effect of channel length modulation and body bias. the values of $\...

The $\text{RC}$ circuit shown below has a variable resistance $R(t)$ given by the following expression:$$R(t)=R_{0}\left(1-\frac{t}{T}\right) \text{for} \:\: 0 \leq t < T...

Consider a unity feedback system, as in the figure shown, with an integral compensator $\dfrac{K}{s}$ and open-loop transfer function$$G(s)=\dfrac{1}{s^{2}+3s+2}$$where $...

Consider the homogenous ordinary differential equation$$x^{2}\frac{d^{2}y}{dx^{2}}-3x\frac{dy}{dx}+3y=0, \quad x>0$$with $y(x)$ as a general solution. Given that$$y(1)=1 ...

Let $h[n]$ be a length – $7$ discrete-time finite impulse response filter, given by$$h[0]=4, \quad h =3,\quad h =2,\quad h[3]=1,$$$$\quad h[-1]=-3, \quad h[-2]=-2, \quad ...

Let a random process $Y(t)$ be described as $Y(t)=h(t) \ast X(t)+Z(t),$ where $X(t)$ is a white noise process with power spectral density $S_{x}(f)=5$W/Hz. The filter $h(...

A voice signal $m(t)$ is in the frequency range $5\:kHz$ to $15\:kHz$. The signal is amplitude-modulated to generated an AM signal $f(t)=A\left(1+m(t)\right)\cos 2\pi f_{...

A random variable $X$ takes values $-1$ and $+1$ with probabilities $0.2$ and $0.8$, respectively. It is transmitted across a channel which adds noise $N,$ so that the ra...

A Germanium sample of dimensions $1\: cm \times 1\: cm$ is illuminated with a $20\:mW,$ $600\: nm$ laser light source as shown in the figure. The illuminated sample surfa...

A rectangular waveguide of width $w$ and height $h$ has cut-off frequencies for $TE_{10}$ and $TE_{11}$ modes in the ration $1:2$ . The aspect ratio $w/h$, rounded off to...

A CMOS inverter, designed to have a mid-point voltage $V_{1}$ equal to half of $V_{dd}.$ as shown in the figure, has the following parameters:$V_{dd}=3V$$\mu_{n} C_{ox}=1...